The Rostrum stands on the Forum Romanum outside the Curia, the assembly of the Roman senate. From this platform Rome's leaders addressed the city's people. Julius Caesar, who reorganised the Forum, decided its final position to be where it still is today.
The commanly used name 'Rostrum' is perhaps not precisely correct, as it should be 'Rostra', a name apparently given to it as it was decorated with the prows of ships (rostra.